Someone here:
has suggested that we’re all falling for a viral marketing gimmick; for a new Xbox game or something.
Maybe some steam punk prop. It resembles a lot of flywheel designs, the edge would be sprockets for a Bendix type starter to engage. The numbers would be pointless though, which is why I think it doesn’t have real utility.
Reddit has a WhatIsThisThing page: https://www.reddit.com/r/whatisthisthing/
It didn’t come up under a search for “iron wheel”, but maybe it’s in there somewhere?
I linked to it earlier in this thread.
http://www.reddit.com/r/Whatisthis/comments/3btyog/strange_numbered_wheel/
On the other hand, the table that the site links to is from a mathematical site http://www.math.tamu.edu/~sottile/research/pages/HopfAlgebras/SSym/F-Product.html where it is labeled Some Combinatorial Hopf Algebras. There is such a thing as a Hopf Algebra; but why that would be engraved on an iron wheel is beyond me.
That was me. (this is my first post on this web site, but been lurking for a long time)
I did some more digging this morning.
making notes to myself as I drink coffee on a lazy sunday morning. (with slight hangover from staying up last night drinking with friends and watching fireworks)
The ssym function I mentioned above is a sophisticated algebra function. (waaaay over my head)
Looking (googling) for more info, I discovered that fancy algebraic function is used in the “Wolfram Language”, a computer programming language.
They write software for lots of thing, including image recognition. And lo and behold, they have a web site to do EXACTLY what we are trying to do, identify a picture of an object.
I put the image of the wheel we’re talking about into that web site and it told me it is an “instrument”. well duh!
Fun circle of events, I start out looking for info on some numbers, that leads me to a web site about an obscure algebra function, that leads me to a programming language that uses it, and that leads me to a web site set up to specifically to do what we’re trying to do, identify an object.
Do I think I’m really onto something here? ,unfortunately no, but it was fun and a kinda interesting ending.
A number of people are linking it to various branches of combinatorics but I don’t think it’s that complicated. Lots of things, and lots of math, involve patterns and the rearrangement of digits, but lots of simpler things also use patterns. There’s no reason that there has to be any deep mathematical reasoning behind this thing and I doubt that someone made a cast iron wheel to illustrate some obscure mathematics.
Correction, teeth, not sprockets, sprockets would be used for a chain drive and that doesn’t look quite right for a chain.
The teeth look like they’ve been finished after casting, I think it would be difficult to cast them and maybe they were ground out entirely after casting. I keep thinking this is someone’s practice piece, maybe made recently at a school or one of tech shops that are popping up. The bottom of the base is corroded, but if that’s cast iron it could corrode rapidly sitting on a damp floor in someone’s basement.
You have Ssym around the wrong way. Ssym is only called that in Wolfram, and that is why you find it called Ssym only in Wolfram. Permutations and Combinations are ordinary things to do, and basically high school maths, and introductory exercises for computer programming students, and the similarity occurs because that is the natural way to do it…
This looks like a heavy engineering version of a lottery wheel.
Actually engineers do random numbers too… they sample one in N of a product for testing…
You do not read the 3 digit or 5 digit or 2 digit number off the wheel , you just take a single digit for each spin… that is why the distribution of the pattern is not important, all that matters is that there are 12 of each digit around the circle.
Using iron wheels for a range of 1 to 5? I’d be surprised if that thing was well balanced enough to produce random results from spinning it.
The ridges on the edge are to make it easier to turn by hand. You need them because the spring on the axle holds the disk firmly in place to wherever you turn it. There are no mounting holes on the base, so it’s not part of some larger piece of machinery – it’s just supposed to sit by itself on a flat surface.
I think it’s some sort of reminder/notation system for use in a factory. Imagine that the settings on a machine are hard to reach – you have to take off the cover plate or something. So when you change the settings, you turn the wheel so the next shift will know how the machinery is configured.
When I consider the numbers in each of the 12 sections I see them as one 8 digit string instead of two separate 3 and 5 digit strings. The only reason they are divided into 3 and 5 digits it to fit all 8 digits into each section.
When viewed that way (as 8 digit strings) what does each section have in common?
Every group contains two 1s, two 2s, two 3s, one 4 and one 5. That seems significant, but I don’t know what the significance is… except that every group of 8 digits adds up to 21.
The “sub-strings” could have been 4 and 4, but 3 and 5 makes more sense because since the stamped digits are so big you can’t stamp all 8 in a row, and a circle naturally gets smaller as you move inward (ergo: 3 digit string inside, 5 digit string outside).
The string lengths would have to be for some reason other than just spacing, considering that the first 3 digits always consist of the digits 1 to 3 and the last 5 always consist of the digits 1 to 5.
Spent far more time than reasonable looking at this.
As noted above, the inner circle of numbers are the set of possible combinations of 1,2,3; of which there are six. But they are not simply two copies, and I suspect that this is actually a mistake. There is some level of symmetry and pattern in the layout, but it only works out if the figure at 5-o-clock is 312 and not 213.
The second row of numbers are 12 of the possible 120 combinations of 1,2,3,4,5. But there is no clear structure to their selection. Curiously four of them are selected from where one might expect them to be - if you take the natural order of the 120 possible selections, numbers 10, 20, 60 and 110, are four of the 12 five digit numbers. But after that it just looks more random. And there is a clear dislike of numbers at the start and end of the sequence. But the numbers are reasonably evenly spread through the ordering.
To my mind it looks a lot like someone wanted to pick 12 numbers from the set, and started by taking the 12 combinations at the 0,10,20,30… locations, and then didn’t like the look of some of them, so chose different ones. (the zero combination is 12345 - so that probably didn’t appeal.) There are also a couple of other very near misses on decade boundaries - which suggests that possibly there were simple mistakes made in enumerating the combinations, and the intend was that most if not all of them were meant to be so selected.
I tend to agree with the suggestions that it is a one off made in a class or other activity, and the design is to some extent simple whimsy. The numbers were probably simply pressed into a sand casting bed. It is easy to make mistakes, and 312 versus 213 all too easy - especially when working around a circle. (I suspect the centre digit was impressed first to provide alignment, and the others added around it.) So some of the other numbers may also have mistakes, making it very hard to divine intent.
Francis,
Good post, after looking into this way more than I should have, I agree with you, it was an experiment, a demo, or a class project of some kind. It’s the numbers chosen, I imagine the builder randomly chose numbers and probably didnt have any numbers greater than 5 because his/her classmate was using them for their project! 
The fact that there is no manufacturer’s mark of any kind, along with the apparent errors, does point to this being some sort of prototype or training project. If that’s the case then we’ll probably never know for sure, unless the original poster (apparently someone on FB) comes forward with some sort of history for the thing.
This is proving to be as mysterious as Amateur Barbarian’s Strange Grid Ball after all!
A little less so because the grid ball was big and a major effort. This wouldn’t have required that much work, much easier to assume it’s just a practice piece.
As pointed out, they were making a wheel from iron and just decided to make some use of it.
It may be a joke present, for example. A memento given to someone when they retired, as he was the workplace gambling man, or had a habit of saying “This is your lucky day” and his nickname was “Lucky”, or something…
I’ve read this thread with interest and just don’t get the impression that this was made as a “practice piece.” The main reason being that the number combinations seem like too much of a pain to put on something done for practice.
The only exception would be if it could be proved to be relatively new and made as a steampunk prop or something. If it’s known to be old, then I don’t see it.
I think the fact that it is a wheel and has a pointer is the main clue. If it were just setting up the two sets of number combinations, I think they would simply have written them down, made a poster to reference, etc.
So the wheel was spun as a type of randomizer. My guess is that it was done for a unique industrial or commercial purpose. I imagine maybe randomizing assortments of goods, such as in boxes of candy.
So I don’t think what it is is knowable unless someone who actually saw it used in its original installation comes forth, which isn’t going to happen.